How to calculate standard error of sample mean

#HOW TO CALCULATE STANDARD ERROR OF SAMPLE MEAN SERIES#

These standard errors may be used to study the significance of the difference between the two means. To calculate the standard errors of the two mean blood pressures, the standard deviation of each sample is divided by the square root of the number of the observations in the sample. Table 1: Mean diastolic blood pressures of printers and farmers For this purpose, she has obtained a random sample of 72 printers and 48 farm workers and calculated the mean and standard deviations, as shown in table 1. However, the concept is that if we were to take repeated random samples from the population, this is how we would expect the mean to vary, purely by chance.Д®xample 1 A general practitioner has been investigating whether the diastolic blood pressure of men aged 20-44 differs between printers and farm workers. It is important to realise that we do not have to take repeated samples in order to estimate the standard error there is sufficient information within a single sample.

If we now divide the standard deviation by the square root of the number of observations in the sample we have an estimate of the standard error of the mean. This is expressed in the standard deviation. We do not know the variation in the population so we use the variation in the sample as an estimate of it. The variation depends on the variation of the population and the size of the sample. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population.ДЄs noted above, if random samples are drawn from a population, their means will vary from one to another.

#HOW TO CALCULATE STANDARD ERROR OF SAMPLE MEAN SERIES#

The series of means, like the series of observations in each sample, has a standard deviation. This can be proven mathematically and is known as the 'Central Limit Theorem'.

These means generally follow a normal distribution, and they often do so even if the observations from which they were obtained do not. If we draw a series of samples and calculate the mean of the observations in each, we have a series of means. Thus the variation between samples depends partly also on the size of the sample. A consequence of this is that if two or more samples are drawn from a population, then the larger they are, the more likely they are to resemble each other - again, provided that the random sampling technique is followed.

In other words, the more people that are included in a sample, the greater chance that the sample will accurately represent the population, provided that a random process is used to construct the sample. Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample. Thus the variation between samples depends partly on the amount of variation in the population from which they are drawn. For example, a series of samples of the body temperature of healthy people would show very little variation from one to another, but the variation between samples of the systolic blood pressure would be considerable. They will show chance variations from one to another, and the variation may be slight or considerable. Resource text Standard error of the meanДЄ series of samples drawn from one population will not be identical. This section considers how precise these estimates may be. The earlier sections covered estimation of statistics. Learning objectives: You will learn about standard error of a mean, standard error of a proportion, reference ranges, and confidence intervals.

How to calculate standard error of sample mean